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  <section id="module-sympy.physics.optics.gaussopt">
<span id="gaussian-optics"></span><h1>Gaussian Optics<a class="headerlink" href="#module-sympy.physics.optics.gaussopt" title="Permalink to this headline">¶</a></h1>
<p>Gaussian optics.</p>
<p>The module implements:</p>
<ul>
<li><p>Ray transfer matrices for geometrical and gaussian optics.</p>
<p>See RayTransferMatrix, GeometricRay and BeamParameter</p>
</li>
<li><p>Conjugation relations for geometrical and gaussian optics.</p>
<p>See geometric_conj*, gauss_conj and conjugate_gauss_beams</p>
</li>
</ul>
<p>The conventions for the distances are as follows:</p>
<dl class="simple">
<dt>focal distance</dt><dd><p>positive for convergent lenses</p>
</dd>
<dt>object distance</dt><dd><p>positive for real objects</p>
</dd>
<dt>image distance</dt><dd><p>positive for real images</p>
</dd>
</dl>
<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">BeamParameter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z_r</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L473-L668"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter" title="Permalink to this definition">¶</a></dt>
<dd><p>Representation for a gaussian ray in the Ray Transfer Matrix formalism.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>wavelen</strong> : the wavelength,</p>
<p><strong>z</strong> : the distance to waist, and</p>
<p><strong>w</strong> : the waist, or</p>
<p><strong>z_r</strong> : the rayleigh range.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">q</span>
<span class="go">1 + 1.88679245283019*I*pi</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">q</span><span class="o">.</span><span class="n">n</span><span class="p">()</span>
<span class="go">1.0 + 5.92753330865999*I</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">w_0</span><span class="o">.</span><span class="n">n</span><span class="p">()</span>
<span class="go">0.00100000000000000</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">z_r</span><span class="o">.</span><span class="n">n</span><span class="p">()</span>
<span class="go">5.92753330865999</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">FreeSpace</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">fs</span> <span class="o">=</span> <span class="n">FreeSpace</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span> <span class="o">=</span> <span class="n">fs</span><span class="o">*</span><span class="n">p</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">w</span><span class="o">.</span><span class="n">n</span><span class="p">()</span>
<span class="go">0.00101413072159615</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">w</span><span class="o">.</span><span class="n">n</span><span class="p">()</span>
<span class="go">0.00210803120913829</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r611"><span class="brackets"><a class="fn-backref" href="#id1">R611</a></span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Complex_beam_parameter">https://en.wikipedia.org/wiki/Complex_beam_parameter</a></p>
</dd>
<dt class="label" id="r612"><span class="brackets"><a class="fn-backref" href="#id2">R612</a></span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Gaussian_beam">https://en.wikipedia.org/wiki/Gaussian_beam</a></p>
</dd>
</dl>
<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.divergence">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">divergence</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.divergence" title="Permalink to this definition">¶</a></dt>
<dd><p>Half of the total angular spread.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">divergence</span>
<span class="go">0.00053/pi</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.gouy">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">gouy</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.gouy" title="Permalink to this definition">¶</a></dt>
<dd><p>The Gouy phase.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">gouy</span>
<span class="go">atan(0.53/pi)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.q">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">q</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.q" title="Permalink to this definition">¶</a></dt>
<dd><p>The complex parameter representing the beam.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">q</span>
<span class="go">1 + 1.88679245283019*I*pi</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.radius">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">radius</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.radius" title="Permalink to this definition">¶</a></dt>
<dd><p>The radius of curvature of the phase front.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">radius</span>
<span class="go">1 + 3.55998576005696*pi**2</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.w">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">w</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.w" title="Permalink to this definition">¶</a></dt>
<dd><p>The beam radius at <span class="math notranslate nohighlight">\(1/e^2\)</span> intensity.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">w</span>
<span class="go">0.001*sqrt(0.2809/pi**2 + 1)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="#sympy.physics.optics.gaussopt.BeamParameter.w_0" title="sympy.physics.optics.gaussopt.BeamParameter.w_0"><code class="xref py py-obj docutils literal notranslate"><span class="pre">w_0</span></code></a></dt><dd><p>The minimal radius of beam.</p>
</dd>
</dl>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.w_0">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">w_0</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.w_0" title="Permalink to this definition">¶</a></dt>
<dd><p>The beam waist (minimal radius).</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">w_0</span>
<span class="go">0.00100000000000000</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="#sympy.physics.optics.gaussopt.BeamParameter.w" title="sympy.physics.optics.gaussopt.BeamParameter.w"><code class="xref py py-obj docutils literal notranslate"><span class="pre">w</span></code></a></dt><dd><p>the beam radius at <span class="math notranslate nohighlight">\(1/e^2\)</span> intensity</p>
</dd>
</dl>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.BeamParameter.waist_approximation_limit">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">waist_approximation_limit</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.BeamParameter.waist_approximation_limit" title="Permalink to this definition">¶</a></dt>
<dd><p>The minimal waist for which the gauss beam approximation is valid.</p>
<p class="rubric">Explanation</p>
<p>The gauss beam is a solution to the paraxial equation. For curvatures
that are too great it is not a valid approximation.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">BeamParameter</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">BeamParameter</span><span class="p">(</span><span class="mf">530e-9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">waist_approximation_limit</span>
<span class="go">1.06e-6/pi</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.CurvedMirror">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">CurvedMirror</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">R</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L317-L344"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.CurvedMirror" title="Permalink to this definition">¶</a></dt>
<dd><p>Ray Transfer Matrix for reflection from curved surface.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>R</strong> : radius of curvature (positive for concave)</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">CurvedMirror</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">R</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;R&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">CurvedMirror</span><span class="p">(</span><span class="n">R</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[   1, 0],</span>
<span class="go">[-2/R, 1]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.CurvedRefraction">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">CurvedRefraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">R</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n2</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L260-L292"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.CurvedRefraction" title="Permalink to this definition">¶</a></dt>
<dd><p>Ray Transfer Matrix for refraction on curved interface.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>R :</strong></p>
<blockquote>
<div><p>Radius of curvature (positive for concave).</p>
</div></blockquote>
<p><strong>n1 :</strong></p>
<blockquote>
<div><p>Refractive index of one medium.</p>
</div></blockquote>
<p><strong>n2 :</strong></p>
<blockquote>
<div><p>Refractive index of other medium.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">CurvedRefraction</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">R</span><span class="p">,</span> <span class="n">n1</span><span class="p">,</span> <span class="n">n2</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;R n1 n2&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">CurvedRefraction</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[               1,     0],</span>
<span class="go">[(n1 - n2)/(R*n2), n1/n2]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.FlatMirror">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">FlatMirror</span></span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L295-L314"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.FlatMirror" title="Permalink to this definition">¶</a></dt>
<dd><p>Ray Transfer Matrix for reflection.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">FlatMirror</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">FlatMirror</span><span class="p">()</span>
<span class="go">Matrix([</span>
<span class="go">[1, 0],</span>
<span class="go">[0, 1]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.FlatRefraction">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">FlatRefraction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n2</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L227-L257"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.FlatRefraction" title="Permalink to this definition">¶</a></dt>
<dd><p>Ray Transfer Matrix for refraction.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>n1 :</strong></p>
<blockquote>
<div><p>Refractive index of one medium.</p>
</div></blockquote>
<p><strong>n2 :</strong></p>
<blockquote>
<div><p>Refractive index of other medium.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">FlatRefraction</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;n1 n2&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">FlatRefraction</span><span class="p">(</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[1,     0],</span>
<span class="go">[0, n1/n2]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.FreeSpace">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">FreeSpace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">d</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L198-L224"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.FreeSpace" title="Permalink to this definition">¶</a></dt>
<dd><p>Ray Transfer Matrix for free space.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>distance</strong></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">FreeSpace</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">d</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;d&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">FreeSpace</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[1, d],</span>
<span class="go">[0, 1]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.GeometricRay">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">GeometricRay</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L382-L466"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.GeometricRay" title="Permalink to this definition">¶</a></dt>
<dd><p>Representation for a geometric ray in the Ray Transfer Matrix formalism.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>h</strong> : height, and</p>
<p><strong>angle</strong> : angle, or</p>
<p><strong>matrix</strong> : a 2x1 matrix (Matrix(2, 1, [height, angle]))</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">GeometricRay</span><span class="p">,</span> <span class="n">FreeSpace</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span><span class="p">,</span> <span class="n">Matrix</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">d</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">angle</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;d, h, angle&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">GeometricRay</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">angle</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[    h],</span>
<span class="go">[angle]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">FreeSpace</span><span class="p">(</span><span class="n">d</span><span class="p">)</span><span class="o">*</span><span class="n">GeometricRay</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">angle</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[angle*d + h],</span>
<span class="go">[      angle]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">GeometricRay</span><span class="p">(</span> <span class="n">Matrix</span><span class="p">(</span> <span class="p">((</span><span class="n">h</span><span class="p">,),</span> <span class="p">(</span><span class="n">angle</span><span class="p">,))</span> <span class="p">)</span> <span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[    h],</span>
<span class="go">[angle]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.GeometricRay.angle">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">angle</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.GeometricRay.angle" title="Permalink to this definition">¶</a></dt>
<dd><p>The angle with the optical axis.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">GeometricRay</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">h</span><span class="p">,</span> <span class="n">angle</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;h, angle&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gRay</span> <span class="o">=</span> <span class="n">GeometricRay</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">angle</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gRay</span><span class="o">.</span><span class="n">angle</span>
<span class="go">angle</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.GeometricRay.height">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">height</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.GeometricRay.height" title="Permalink to this definition">¶</a></dt>
<dd><p>The distance from the optical axis.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">GeometricRay</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">h</span><span class="p">,</span> <span class="n">angle</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;h, angle&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gRay</span> <span class="o">=</span> <span class="n">GeometricRay</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">angle</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gRay</span><span class="o">.</span><span class="n">height</span>
<span class="go">h</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.RayTransferMatrix">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">RayTransferMatrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L53-L195"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Base class for a Ray Transfer Matrix.</p>
<p>It should be used if there isn’t already a more specific subclass mentioned
in See Also.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>parameters :</strong></p>
<blockquote>
<div><p>A, B, C and D or 2x2 matrix (Matrix(2, 2, [A, B, C, D]))</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">RayTransferMatrix</span><span class="p">,</span> <span class="n">ThinLens</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Symbol</span><span class="p">,</span> <span class="n">Matrix</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RayTransferMatrix</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span>
<span class="go">Matrix([</span>
<span class="go">[1, 2],</span>
<span class="go">[3, 4]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">RayTransferMatrix</span><span class="p">(</span><span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]]))</span>
<span class="go">Matrix([</span>
<span class="go">[1, 2],</span>
<span class="go">[3, 4]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">A</span>
<span class="go">1</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">f</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">lens</span> <span class="o">=</span> <span class="n">ThinLens</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">lens</span>
<span class="go">Matrix([</span>
<span class="go">[   1, 0],</span>
<span class="go">[-1/f, 1]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">lens</span><span class="o">.</span><span class="n">C</span>
<span class="go">-1/f</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.GeometricRay" title="sympy.physics.optics.gaussopt.GeometricRay"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GeometricRay</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.BeamParameter" title="sympy.physics.optics.gaussopt.BeamParameter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BeamParameter</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.FreeSpace" title="sympy.physics.optics.gaussopt.FreeSpace"><code class="xref py py-obj docutils literal notranslate"><span class="pre">FreeSpace</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.FlatRefraction" title="sympy.physics.optics.gaussopt.FlatRefraction"><code class="xref py py-obj docutils literal notranslate"><span class="pre">FlatRefraction</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.CurvedRefraction" title="sympy.physics.optics.gaussopt.CurvedRefraction"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CurvedRefraction</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.FlatMirror" title="sympy.physics.optics.gaussopt.FlatMirror"><code class="xref py py-obj docutils literal notranslate"><span class="pre">FlatMirror</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.CurvedMirror" title="sympy.physics.optics.gaussopt.CurvedMirror"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CurvedMirror</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.ThinLens" title="sympy.physics.optics.gaussopt.ThinLens"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ThinLens</span></code></a></p>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r613"><span class="brackets"><a class="fn-backref" href="#id3">R613</a></span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis">https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis</a></p>
</dd>
</dl>
<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.RayTransferMatrix.A">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">A</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.RayTransferMatrix.A" title="Permalink to this definition">¶</a></dt>
<dd><p>The A parameter of the Matrix.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">RayTransferMatrix</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RayTransferMatrix</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">A</span>
<span class="go">1</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.RayTransferMatrix.B">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">B</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.RayTransferMatrix.B" title="Permalink to this definition">¶</a></dt>
<dd><p>The B parameter of the Matrix.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">RayTransferMatrix</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RayTransferMatrix</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">B</span>
<span class="go">2</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.RayTransferMatrix.C">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">C</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.RayTransferMatrix.C" title="Permalink to this definition">¶</a></dt>
<dd><p>The C parameter of the Matrix.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">RayTransferMatrix</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RayTransferMatrix</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">C</span>
<span class="go">3</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.RayTransferMatrix.D">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">D</span></span><a class="headerlink" href="#sympy.physics.optics.gaussopt.RayTransferMatrix.D" title="Permalink to this definition">¶</a></dt>
<dd><p>The D parameter of the Matrix.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">RayTransferMatrix</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span> <span class="o">=</span> <span class="n">RayTransferMatrix</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mat</span><span class="o">.</span><span class="n">D</span>
<span class="go">4</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.ThinLens">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">ThinLens</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L347-L375"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.ThinLens" title="Permalink to this definition">¶</a></dt>
<dd><p>Ray Transfer Matrix for a thin lens.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>f :</strong></p>
<blockquote>
<div><p>The focal distance.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">ThinLens</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">ThinLens</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
<span class="go">Matrix([</span>
<span class="go">[   1, 0],</span>
<span class="go">[-1/f, 1]])</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.RayTransferMatrix" title="sympy.physics.optics.gaussopt.RayTransferMatrix"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RayTransferMatrix</span></code></a></p>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.conjugate_gauss_beams">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">conjugate_gauss_beams</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wavelen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">waist_in</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">waist_out</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L830-L891"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.conjugate_gauss_beams" title="Permalink to this definition">¶</a></dt>
<dd><p>Find the optical setup conjugating the object/image waists.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>wavelen :</strong></p>
<blockquote>
<div><p>The wavelength of the beam.</p>
</div></blockquote>
<p><strong>waist_in and waist_out :</strong></p>
<blockquote>
<div><p>The waists to be conjugated.</p>
</div></blockquote>
<p><strong>f :</strong></p>
<blockquote>
<div><p>The focal distance of the element used in the conjugation.</p>
</div></blockquote>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>a tuple containing (s_in, s_out, f)</p>
<p>s_in :</p>
<blockquote>
<div><p>The distance before the optical element.</p>
</div></blockquote>
<p>s_out :</p>
<blockquote>
<div><p>The distance after the optical element.</p>
</div></blockquote>
<p>f :</p>
<blockquote>
<div><p>The focal distance of the optical element.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">conjugate_gauss_beams</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span><span class="p">,</span> <span class="n">factor</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">l</span><span class="p">,</span> <span class="n">w_i</span><span class="p">,</span> <span class="n">w_o</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;l w_i w_o f&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">conjugate_gauss_beams</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">w_i</span><span class="p">,</span> <span class="n">w_o</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">f*(1 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)))</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">factor</span><span class="p">(</span><span class="n">conjugate_gauss_beams</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">w_i</span><span class="p">,</span> <span class="n">w_o</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">)[</span><span class="mi">1</span><span class="p">])</span>
<span class="go">f*w_o**2*(w_i**2/w_o**2 - sqrt(w_i**2/w_o**2 -</span>
<span class="go">          pi**2*w_i**4/(f**2*l**2)))/w_i**2</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">conjugate_gauss_beams</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">w_i</span><span class="p">,</span> <span class="n">w_o</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span>
<span class="go">f</span>
</pre></div>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.gaussian_conj">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">gaussian_conj</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s_in</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z_r_in</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L782-L827"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.gaussian_conj" title="Permalink to this definition">¶</a></dt>
<dd><p>Conjugation relation for gaussian beams.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>s_in :</strong></p>
<blockquote>
<div><p>The distance to optical element from the waist.</p>
</div></blockquote>
<p><strong>z_r_in :</strong></p>
<blockquote>
<div><p>The rayleigh range of the incident beam.</p>
</div></blockquote>
<p><strong>f :</strong></p>
<blockquote>
<div><p>The focal length of the optical element.</p>
</div></blockquote>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>a tuple containing (s_out, z_r_out, m)</p>
<p>s_out :</p>
<blockquote>
<div><p>The distance between the new waist and the optical element.</p>
</div></blockquote>
<p>z_r_out :</p>
<blockquote>
<div><p>The rayleigh range of the emergent beam.</p>
</div></blockquote>
<p>m :</p>
<blockquote>
<div><p>The ration between the new and the old waists.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">gaussian_conj</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">s_in</span><span class="p">,</span> <span class="n">z_r_in</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;s_in z_r_in f&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">gaussian_conj</span><span class="p">(</span><span class="n">s_in</span><span class="p">,</span> <span class="n">z_r_in</span><span class="p">,</span> <span class="n">f</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">1/(-1/(s_in + z_r_in**2/(-f + s_in)) + 1/f)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">gaussian_conj</span><span class="p">(</span><span class="n">s_in</span><span class="p">,</span> <span class="n">z_r_in</span><span class="p">,</span> <span class="n">f</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>
<span class="go">z_r_in/(1 - s_in**2/f**2 + z_r_in**2/f**2)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">gaussian_conj</span><span class="p">(</span><span class="n">s_in</span><span class="p">,</span> <span class="n">z_r_in</span><span class="p">,</span> <span class="n">f</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span>
<span class="go">1/sqrt(1 - s_in**2/f**2 + z_r_in**2/f**2)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.geometric_conj_ab">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">geometric_conj_ab</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L718-L746"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.geometric_conj_ab" title="Permalink to this definition">¶</a></dt>
<dd><p>Conjugation relation for geometrical beams under paraxial conditions.</p>
<p class="rubric">Explanation</p>
<p>Takes the distances to the optical element and returns the needed
focal distance.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">geometric_conj_ab</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;a b&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">geometric_conj_ab</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">a*b/(a + b)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.geometric_conj_af" title="sympy.physics.optics.gaussopt.geometric_conj_af"><code class="xref py py-obj docutils literal notranslate"><span class="pre">geometric_conj_af</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.geometric_conj_bf" title="sympy.physics.optics.gaussopt.geometric_conj_bf"><code class="xref py py-obj docutils literal notranslate"><span class="pre">geometric_conj_bf</span></code></a></p>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.geometric_conj_af">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">geometric_conj_af</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L749-L777"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.geometric_conj_af" title="Permalink to this definition">¶</a></dt>
<dd><p>Conjugation relation for geometrical beams under paraxial conditions.</p>
<p class="rubric">Explanation</p>
<p>Takes the object distance (for geometric_conj_af) or the image distance
(for geometric_conj_bf) to the optical element and the focal distance.
Then it returns the other distance needed for conjugation.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics.gaussopt</span> <span class="kn">import</span> <span class="n">geometric_conj_af</span><span class="p">,</span> <span class="n">geometric_conj_bf</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;a b f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">geometric_conj_af</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
<span class="go">a*f/(a - f)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">geometric_conj_bf</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
<span class="go">b*f/(b - f)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.geometric_conj_ab" title="sympy.physics.optics.gaussopt.geometric_conj_ab"><code class="xref py py-obj docutils literal notranslate"><span class="pre">geometric_conj_ab</span></code></a></p>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.geometric_conj_bf">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">geometric_conj_bf</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L749-L777"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.geometric_conj_bf" title="Permalink to this definition">¶</a></dt>
<dd><p>Conjugation relation for geometrical beams under paraxial conditions.</p>
<p class="rubric">Explanation</p>
<p>Takes the object distance (for geometric_conj_af) or the image distance
(for geometric_conj_bf) to the optical element and the focal distance.
Then it returns the other distance needed for conjugation.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics.gaussopt</span> <span class="kn">import</span> <span class="n">geometric_conj_af</span><span class="p">,</span> <span class="n">geometric_conj_bf</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;a b f&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">geometric_conj_af</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
<span class="go">a*f/(a - f)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">geometric_conj_bf</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
<span class="go">b*f/(b - f)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.geometric_conj_ab" title="sympy.physics.optics.gaussopt.geometric_conj_ab"><code class="xref py py-obj docutils literal notranslate"><span class="pre">geometric_conj_ab</span></code></a></p>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.rayleigh2waist">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">rayleigh2waist</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z_r</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelen</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L697-L715"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.rayleigh2waist" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate the waist from the rayleigh range of a gaussian beam.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">rayleigh2waist</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">z_r</span><span class="p">,</span> <span class="n">wavelen</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;z_r wavelen&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">rayleigh2waist</span><span class="p">(</span><span class="n">z_r</span><span class="p">,</span> <span class="n">wavelen</span><span class="p">)</span>
<span class="go">sqrt(wavelen*z_r)/sqrt(pi)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.waist2rayleigh" title="sympy.physics.optics.gaussopt.waist2rayleigh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">waist2rayleigh</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.BeamParameter" title="sympy.physics.optics.gaussopt.BeamParameter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BeamParameter</span></code></a></p>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="sympy.physics.optics.gaussopt.waist2rayleigh">
<span class="sig-prename descclassname"><span class="pre">sympy.physics.optics.gaussopt.</span></span><span class="sig-name descname"><span class="pre">waist2rayleigh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">w</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wavelen</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/optics/gaussopt.py#L675-L694"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.optics.gaussopt.waist2rayleigh" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate the rayleigh range from the waist of a gaussian beam.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.optics</span> <span class="kn">import</span> <span class="n">waist2rayleigh</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">w</span><span class="p">,</span> <span class="n">wavelen</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;w wavelen&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">waist2rayleigh</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">wavelen</span><span class="p">)</span>
<span class="go">pi*w**2/wavelen</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.physics.optics.gaussopt.rayleigh2waist" title="sympy.physics.optics.gaussopt.rayleigh2waist"><code class="xref py py-obj docutils literal notranslate"><span class="pre">rayleigh2waist</span></code></a>, <a class="reference internal" href="#sympy.physics.optics.gaussopt.BeamParameter" title="sympy.physics.optics.gaussopt.BeamParameter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BeamParameter</span></code></a></p>
</div>
</dd></dl>

</section>


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